1. Find the average value of :

on the interval

Work: I know the formula is 1/(b - a) * ∫ f(x) dx (from x=a to b).

so I got (1/ (13pi/6))

Integrated 4sinx+7cosx= 4-cosx+7sinx, plugged in (13pi/6) and also 0 and subtracted them.

((13pi/6))[((4-cos((13pi/6))+7sin((13pi/6))))-((4-cos(0)+7sin(0)))]

But that is wrong...

2.find the average value of on the interval

same as above, it is (1/1)* integral of cos^4xsinx [from 0 to 1]

intregal of cos^4xsinx =(3+4cos(2x)+cos(4x))/8 -cosx

(3+4cos(2)+cos(4))/8*-cos1-(3+4cos(0)+cos(0))/8*-cos0